/// <summary>
/// Gets a matrix determinant.
/// </summary>
/// <returns>
/// Returns the matrix determinant.
/// </returns>
public double Determinant()
{
if (!IsSquare)
{
throw new NonSquareMatrixException("Attempt to find a determinant of a non square matrix");
}
if (Rows == 2 && Columns == 2)
{
return(Determinant2x2());
}
if (Rows == 3 && Columns == 3)
{
return(Determinant3x3());
}
double determinant = 1;
var luDecomposition = new LupDecomposition();
var(c, _) = luDecomposition.Decompose(this);
for (int i = 0; i < c.Rows; i++)
{
determinant *= c[i, i];
}
return(determinant);
}
/// <summary>
/// Solves a system of linear equations, <b>Ax = b</b>.
/// </summary>
/// <param name="factor">A coefficient matrix A.</param>
/// <param name="right">A right-hand vector b.</param>
/// <returns>
/// Returns a vector x that is a solution of the system of linear equations, <b>Ax = b</b>.
/// </returns>
public Vector Solve(Matrix factor, Vector right)
{
if (factor == null)
{
throw new ArgumentNullException("Factor matrix cannot be null.");
}
if (right == null)
{
throw new ArgumentNullException("Right vector cannot be null.");
}
if (factor.Rows != right.Size)
{
throw new ArgumentException("Factor matrix and right vector have inconsistence size.");
}
var decomposition = new LupDecomposition();
var(c, p) = decomposition.Decompose(factor);
var y = SolveLower(c, p * right);
var x = SolveUpper(c, y);
return(x);
}
public void LupDecomposition_CalculateLUMatrices_ReturnsAsExpected()
{
var lupDecomposition = new LupDecomposition();
var matrix = new Matrix(4, 4,
new double[, ] {
{ 2, 1, 1, 0 }, { 4, 3, 3, 1 }, { 8, 7, 9, 5 }, { 6, 7, 9, 8 }
});
var expectedC = new Matrix(4, 4,
new double[, ] {
{ 8, 7, 9, 5 }, { 0.75, 1.75, 2.25, 4.25 }, { 0.5, -0.28571, -0.85714, -0.28571 }, { 0.25, -0.42857, 0.33333, 0.66667 }
});
var expectedP = new Matrix(4, 4,
new double[, ] {
{ 0, 0, 1, 0 }, { 0, 0, 0, 1 }, { 0, 1, 0, 0 }, { 1, 0, 0, 0 }
});
var(c, p) = lupDecomposition.Decompose(matrix);
Assert.That(c.Cast <double>(), Is.EqualTo(expectedC.Cast <double>()).Within(0.00001));
Assert.AreEqual(expectedP, p);
}
